AdS/CFT and gravity

The radiation-dominated $k=0\mathrm{}$ FRW cosmology emerges as the induced metric on a codimension one hypersurface of constant extrinsic curvature in the five-dimensional AdS-Schwarzschild solution. That we should get FRW cosmology in this way is an expected result from AdS/CFT in light of recent comments regarding the coupling of gravity to “boundary” conformal field theories. I remark on how this calculation bears on the understanding of the Randall-Sundrum “alternative to compactification.” A generalization of the AdS/CFT prescription for computing Green’s functions is suggested, and it is shown how gravity emerges from it with a strength $G_4{=2G}_5/L.\mathrm{}$ Some upper bounds are set on the radius of curvature L of ${\mathrm{AdS}}_5.$ One of them comes from estimating the rate of leakage of visible sector energy into the CFT. That rate is connected via a unitarity relation to deviations from Newton’s force law at short distances. The best bound on L obtained in this paper comes from a match to the parameters of string theory. It is $L\lesssim 1\mathrm{nm}$ if the string scale is $1\mathrm{GeV}.$ Higher string scales imply a tighter bound on L.